The sampling and full reconstruction of band-limited signals at sub-Nyquist rates

Methods by which bandlimited signals may be sampled at sub-Nyquist rates and fully recovered are presented. The realization of these methods requires a reconstruction network that is more complex than a simple low-pass filter. These recovery techniques make use of the fact that the aliasing frequency spectra arising from sub-Nyquist sampling is known and can be duplicated. it is proven that the time-domain product (double sideband amplitude modulation) of the analog input with a sinusoidal carrier version of the sampling clock is proportional to the aliasing spectra for impulse and finite pulsewidth sampling systems. A proof of reconstruction for the digital input with finite pulsewidth sampling is also given